Assignment 14

course Mth 151

I have had a difficult time with Ch 3 so far, any suggestions.

????????????assignment #014014. `query 14

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College Algebra

10-14-2007

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12:06:36

3.3.5 rewrite using if then ' all marines love boot camp '.

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RESPONSE -->

If you are a marine, then you love boot camp.

confidence assessment: 3

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12:08:37

** The statement is equivalent to 'If it's a Marine, it loves boot camp' or equivalent.

The statement is not equivalent to 'if it is boot camp, then all Marines love it', which is the converse of the original statement. **

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RESPONSE -->

self critique assessment: 2

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12:11:20

3.3.18 ~p false q false p -> q true

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RESPONSE -->

If ~p is false and q is false, then p -> q is true.

confidence assessment: 2

~p -> q would be true, but p -> q would be of the form T -> F, and would be false.

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12:13:07

** Since ~p is false then p is true.

Since q is false it follows that p -> q is of the form T -> F, which is false.

The conditional is false when, and only when, the antecedent is true and the consequent false. **

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RESPONSE -->

I thought I was suppose to change the statement into an if, then statement.

self critique assessment: 2

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12:17:26

Query 3.3.36 write in symbols 'If we don't bike, then it does not rain.'

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RESPONSE -->

~b -> ~r

confidence assessment: 3

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12:19:08

** If p stands for 'don't bike' and r for 'it rains' then the statement would be p -> ~q. **

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RESPONSE -->

The book says b stands for ""I ride my bike and r ""it rains. With these symbols, would my compound statement be correct?

self critique assessment: 2

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12:26:22

Query 3.3.48 q true, p and r false, evaluate and (-r U p) -> p

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RESPONSE -->

True.

confidence assessment: 1

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12:39:51

Query 3.3.60 truth table for (p ^ q) -> (p U q)

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RESPONSE -->

True - tautology.

confidence assessment: 3

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12:41:30

** The headings would be p, q ,(p^q), (pUq), (p^q)->(pUq)

Row 1 would read T T T T T

Row 2 would read T F F T T

Row 3 would read F T F T T

Row 4 would read F F F F T

The common sense of this is that whenever both p and q are true, then the statement 'p or q' must be true. That's what means to say (p ^ q) -> (p U q).

The fact that this statement is true is indicated by the last column of the truth table, which has True in every possible case. **

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RESPONSE -->

I came out with all true so I put tautology since they were all ture.

self critique assessment: 2

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12:48:48

Query 3.3.74 (formerly 3.3.72). This wasn't assigned but it is similar to assigned questions and should be answered: What is the negation of the statement 'if loving you is wrong then I don't want to be right' ?

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RESPONSE -->

Loving you is wrong and it isn't right.

confidence assessment: 1

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12:49:52

** The negation has to have the exact opposite truth values of the original statement.

It is difficult and confusing to try to negate a conditional. It is much easier to translate the conditional to a disjunction then negate the disjunction. It is easy to negate the disjunction using deMorgan's Laws.

Since p -> q is identical to ~p U q, the negation of p -> q is ~ ( ~p U q), which by de Morgan's Law is ~ ~p ^ ~q, or just p ^ ~q.

So the negation would ge 'loving you is wrong AND I want to be right.

COMMON ERROR AND NOTE: If loving you is wrong, then I want to be right.

INSTRUCTOR COMMENT:

The negation of a conditional can't be a conditional (a conditional is false in only one case so its negation would have to be false in three cases). **

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RESPONSE -->

I hope what I said was pretty much the same thing.

self critique assessment: 1

Close, but 'I wan't to be right' isn't the same thing as 'isn't right'.

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You're not doing badly. More detail about your thinking and your solution process would give me enough information to make additional suggestions. You're welcome to go back into any submission and insert additional information on the process and especially additional self-critiques (if you do mark insertions with &&&&) and I'll be glad to comment further.